There is a growing interest in attempting to study cognitive and social phenomena under the umbrella of "complex theory". We are indeed immersed in so-called "complex systems", but we are still a long way from a clear understanding of the concepts and principles that underlie the "complexity thinking" . The purpose of this paper to provide a simple (and too short) conceptual framework to understand the basic ideas that allow us to think and speak of complexity in the context of PERPLEXUS as a physical substratum for the embodiment of questions related to cognition (individual and/or social) and the material realization of philosophical thought-experiments. To do so, we will notice the controversies concerning the very existence of such a thing as a "theory of complexity". We also will capture some features that can be considered as characterizations (or fingerprints) of "complexity thinking" by contrasting them with a classical Cartesian-Newtonian mode of thinking. Then, we will stress the key role of embodiment as a necessary ingredient to be incorporated in the explanatory efforts of different domains dealing with cognition, development and evolution. We will finally explain how the platform PERPLEXUS can represent such an ideal locus for reformatting and tackling conceptual and philosophical questions grounded in aspects of complexity and embodiment.